Activity & The Decay Constant (OCR A Level Physics)

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Katie M


Katie M



Activity & The Decay Constant

  • Since radioactive decay is spontaneous and random, it is useful to consider the average number of nuclei which are expected to decay per unit time
    • This is known as the average decay rate

  • As a result, each radioactive element can be assigned a decay constant
  • The decay constant λ is defined as:

The probability, per second, that a given nucleus will decay

  • When a sample is highly radioactive, this means the number of decays per unit time is very high
    • This suggests it has a high level of activity

  • Activity, or the number of decays per unit time can be calculated using:

Activity & The Decay Constant equation 1

  • Where:
    • A = activity of the sample (Bq)
    • ΔN = number of decayed nuclei
    • Δt = time interval (s)
    • λ = decay constant (s-1)
    • N = number of nuclei remaining in a sample

  • The activity of a sample is measured in Becquerels (Bq)
    • An activity of 1 Bq is equal to one decay per second, or 1 s-1

  • This equation shows:
    • The greater the decay constant, the greater the activity of the sample
    • The activity depends on the number of undecayed nuclei remaining in the sample
    • The minus sign indicates that the number of nuclei remaining decreases with time - however, for calculations it can be omitted

Worked example

Americium-241 is an artificially produced radioactive element that emits α-particles. A sample of americium-241 of mass 5.1 μg is found to have an activity of 5.9 × 105 Bq.

Determine the number of nuclei in the sample of americium-241.
Determine the decay constant of americium-241.

Part (a)

Step 1: Write down the known quantities

      • Mass = 5.1 μg = 5.1 × 10-6 g
      • Molecular mass of americium = 241
      • NA = Avogadro constant

Step 2: Write down the equation relating number of nuclei, mass and molecular mass

Activity & The Decay Constant Worked Example equation 1

Step 3: Calculate the number of nuclei

Activity & The Decay Constant Worked Example equation 2

Part (b)

Step 1: Write the equation for activity

Activity, A = λN

Step 2: Rearrange for decay constant λ and calculate the answer

Activity & The Decay Constant Worked Example equation 3

Exam Tip

There are lots of new symbols and definitions in this unit. Make sure you are clear on what each symbol means.

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Katie M

Author: Katie M

Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.

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